weighting the residuals by the covariance matrix \(\Gamma \)  of the synthetic data. Figure
REF (a) shows the residual as a function of EKI iteration. The residual decreases quickly over the first few iterations, before plateauing for subsequent
iterations. Figure
REF (b) shows standard deviations of the ensemble of parameters. The standard deviations decrease monotonically from iteration to iteration, reflecting the evolution
toward consensus. The behavior is qualitatively similar for all realizations; quantitative differences reflect different realizations of internal variability in the different data realizations. This behavior reflects the fact that EKI is
an optimization method for calibrating parameters: it is not
constructed to learn uncertainty but rather to reach consensus around a single parameter value that makes the misfit small
[1]}.
